Tethered jailbreak for any iPod touch (2nd generation) with the new bootrom. Untethered for the old bootrom. Star can be modified to support 4.0.2-4.3, because Apple did not correctly patch the exploits used.
Some of the most popular programs for jailbreaking an iPod Touch 2G are limera1n (Limerain), Redsn0w (Redsnow), and GreenPois0n (GreenPoison), which can be downloaded from Guide My Jailbreak. Note that Redsn0w is compatible with iOS 4.2.1 and the MB model